3 Answers
3

There was just a post today on Language Log about constructions like this, known as absolutives. In it, Mark Liberman quotes from the Cambridge Grammar of the English Language:

pages 1265-6 of CGEL, where the followed two examples are given:

His hands gripping the door, he let out a volley of curses.This done, she walked off without another word.

...
The [italicized] non-finites are supplements with the main clause as anchor. [The examples shown] contain a subject, and belong to what is known as the absolute construction, one which is subordinate in form but with no syntactic link to the main clause. […]

In [none of these examples] is there any explicit indication of the semantic relation between the supplement and the anchor. This has to be inferred from the content of the clauses and/or the context.

A comma splice, on the other hand, is when two sentences are connected with a comma instead of a period.